Subgroups — #13097895

Order 1600.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₂₅	C₂	1	1	yes	maximal, characteristic
2	#11716407	C₂	1	1	yes	maximal, characteristic
3	#11716406	C₂	1	1	yes	maximal, characteristic
4	Q₈×D₂₅	—	2	1	no	—
5	#87735	—	2	1	no	—
6	Q₁₆×C₂₅	C₄	1	1	yes	characteristic
7	#87723	—	2	1	no	—
8	C₈×D₂₅	C₂²	1	1	yes	characteristic
9	Dic₁₀₀	C₄	1	1	yes	characteristic
10	#87709	—	2	1	no	—
11	#64910	—	5	1	no	maximal
12	Q₈×C₂₅	—	2	1	no	—
13	C₄×D₂₅	—	4	1	no	—
14	C₄×D₂₅	D₄	1	1	yes	characteristic
15	Dic₅₀	—	2	1	no	—
16	Dic₅₀	—	4	1	no	—
17	#6016	—	4	1	no	—
18	C₈×C₂₅	C₂×C₄	1	1	yes	characteristic
19	#6014	D₄	1	1	yes	characteristic
20	D₅×Q₁₆	—	5	1	no	—
21	#3995	—	5	1	no	—
22	#3990	—	5	1	no	—
23	C₂×D₂₅	SD₁₆	1	1	yes	characteristic
24	C₄×C₂₅	—	4	1	no	—
25	C₄×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₂₅	—	4	1	no	—
27	Dic₂₅	D₈	1	1	yes	characteristic
28	Q₈×D₅	—	10	1	no	—
29	#700	—	10	1	no	—
30	C₅×Q₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
31	#689	—	10	1	no	—
32	Dic₂₀	—	5	1	no	—
33	C₈×D₅	—	5	1	no	—
34	#674	—	10	1	no	—
35	#362	—	25	1	no	Sylow
36	C₂×C₂₅	#102	1	1	yes	characteristic
37	D₂₅	—	2	1	no	—
38	C₅×Q₈	—	2	1	no	—
39	C₄×D₅	—	5	1	no	—
40	C₄×D₅	—	20	1	no	—
41	Dic₁₀	—	10	1	no	—
42	Dic₁₀	—	20	1	no	—
43	#170	—	20	1	no	—
44	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
45	#168	—	5	1	no	—
46	C₂×Q₁₆	—	25	1	no	—
47	M₃₂	—	25	1	no	—
48	#108	—	25	1	no	—
49	C₂₅	#362	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₅	—	5	1	no	—
51	C₄×C₅	—	4	1	no	—
52	C₄×C₅	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
53	Dic₅	—	5	1	no	—
54	Dic₅	—	20	1	no	—
55	C₂×Q₈	—	50	1	no	—
56	Q₁₆	—	25	1	no	—
57	Q₁₆	—	50	1	no	—
58	Q₁₆	#1035	1	1	yes	characteristic
59	M₁₆	—	50	1	no	—
60	C₂×C₈	—	25	1	no	—
61	C₁₆	—	50	1	no	—
62	C₂×C₅	#4007	1	1	yes	characteristic
63	D₅	—	10	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	50	1	no	—
66	Q₈	—	100	1	no	—
67	C₂×C₄	—	25	1	no	—
68	C₂×C₄	—	100	1	no	—
69	C₈	—	25	1	no	—
70	C₈	—	100	1	no	—
71	C₈	C₂×#1035	1	1	yes	characteristic
72	C₅	#64910	1	1	yes	characteristic
73	C₂²	—	25	1	no	—
74	C₄	—	4	1	no	—
75	C₄	—	25	1	no	—
76	C₄	—	100	1	no	—
77	C₄	C₂²⋊#1035	1	1	yes	characteristic
78	C₂	—	50	1	no	—
79	C₂	#11716424	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716424
commutator	C₈×C₂₅	C₂×C₄
Frattini	C₅×C₈	C₂×AGL(1,𝔽₅)
Fitting	Q₁₆×C₂₅	C₄
socle	C₂×C₅	#4007
prime radical	C₂×D₂₅	SD₁₆
cosocle	C₈×D₂₅	C₂²
hypercenter	Q₁₆	#1035
hypocenter	C₂₅	#362
LCS	G ▷ C₈×C₂₅ ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
49. C₂₅	#362	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₁₆×D₂₅	2
#11716407	2
#11716406	2
#64910	5